Men greeting Men – A handshake is appropriate in most situations.  Handshakes tend to be energetic and very often linger a bit.  To express extra deference, the hand-shaker may lightly grip his hand-shaking forearm with the opposite hand.  Many times men will hold hands with other men, and often the handshake is prolonged into this hand-holding. This does not have any implication on their sexual preferences; it's just a sign of friendship and closeness.

Women greeting Women – A handshake and/or nod of acknowledgment is appropriate in most situations.  If you would like to show great respect you may also place your left hand over your right elbow/forearm when handshaking. Many times women will hold hands with other women, and often the handshake is prolonged into this hand-holding. 

Meetings between Men and Women – Appropriate greetings depend on the nature of the relationship and region. A handshake is usually appropriate but it is best to wait for the woman to extend her hand, otherwise a bow or a nod of acknowledgment will suffice.

Note: Always use your right hand when shaking hands.